If so, I don't understand why the Sue de Coq approach misses an elimination that the doubly-linked ALS makes.

The eliminations should be the same. They should also be the same as for the partially and fully complementary patterns using SIS 26b7. R7c6<>4 is left out as a direct elimination here too. I'm not saying a player should ignore a follow-on locked candidate move, just recognize that it is one, at least once in a while.

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Luke451 wrote:

I realize this isn't a really good example, as r8c1<>4 also takes care of (4)r7c6 in the wash. Still, if one approach finds additional eliminations over the other, why even use the other?

Such a "wash" would always be the case in a practical example.

[edits: 1) added images; 2) narrow the 2nd image]

Last edited by ronk on Thu Jun 28, 2012 8:03 pm; edited 2 times in total

The original SDC pattern examples, including my own (http://forum.enjoysudoku.com/sue-de-coq-revisited-again-asi-1-t6410.html) were such that the digits in the 'outlying cells' (in this case,(26)r3c3 and (347)r7c12) were also present in the 'core' aals or aaals (in this case, (2367)r89c3). However, more recently, examples of 'extended' SDCs such as the one above have been described where the 4s in r89c3, not present in the 'core', allow the usual eliminations of a SDC, but also add eliminations of all 4s within the same box as r7c12.

As far as the issue of r7c6<>4 goes. Theoretically, based on the issue that a SDC is simply an expression of a DL-ALS, r7c6 should be <>4, but in practice it can cause confusion for the manual pattern solver since the eliminations from the other digits in r7c12 apply only to the same box.

'IMO' applies to all of the following:
Patterns such as SDC were meant to aid the manual pattern solver to find eliminations. It was never originally described as an alternate way to find DL-ALS patterns. While I find Aran's premise that, approached a certain way, DL-ALS patterns should be just as easy as corresponding SDCs interesting, on further thought and review, I disagree. The written rules for finding an SDC may seem obscure, but when you see practical examples, the pattern is relatively easy and straightforward for pattern solvers such as myself. The DL-ALS, not so much.

So, I have no problem with an 'extended' SDC not allowing for an elimination such as r7c6<>4. If a manual solver is skilled enough to add it then good for him/her. As to the question why use one pattern over the other if one of them potentially provides more eliminations: If the one that provides more eliminations is far less likely to be found by manual solvers than the other, then it's advantage is more theoretical than practical. Besides, the situation in question in this SDC is relatively rare.

(Btw: You can also have an 'extended' SDC where digits (commensurate with a valid 'extended' SDC) in the outlying row or column (as the case may be) outlying cells are not in the 'core' aals and aaals. All same-value digits in that row or column (outside of the 'core') can be eliminated.)

Last edited by DonM on Thu Jun 28, 2012 7:53 pm; edited 5 times in total

I'm not saying a player should ignore a follow-on locked candidate move, just recognize that it is one, at least once in a while.

The simplicity of DL-ALS - apart even from the definition - lies in the elimination rule :
any candidate which reduces EITHER ALS to a locked set is false.
There is no hierarchy among those candidates.
In the example 4r8c1 and 4r7c6 SEPARATELY, INDEPENDENTLY and...admirably...qualify as eliminations.

I'm not saying a player should ignore a follow-on locked candidate move, just recognize that it is one, at least once in a while.

There is no hierarchy among those candidates.
In the example 4r8c1 and 4r7c6 SEPARATELY, INDEPENDENTLY and...admirably...qualify as eliminations.

Perhaps too subtle for someone who has argued that an almost-naked-pair is a hidden-pair but, in my book, "SEPARATELY, INDEPENDENTLY" indicates follow-on action of some sort. For this single ALS, e.g., there are two scans for eliminations, once in a box and once in a line. One scan follows the other.